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Unformatted text preview: Trigonometric Equations Trigonometric equations are equations involving trigonometric functions. A trigonometric equation can involve one or more trigonometric functions. Solving the trigonometric equation means finding all the angles that satisfy the equation. Example π θ θ 2 , 2 3 sin : equation the Solve ≤ ≤ = We want all angles in one revolution having sine equal to the value given. Sine is positive in quadrants 1 and 2, so there are two answers. What is the reference angle of θ? . 3 in angle reference the , 2 3 sin Since π θ = In Quadrant I, an angle is its own reference angle, so our first answer is 3 π θ = In Quadrant II, the angle is obtained by subtracting the reference angle from π, so our second answer is 3 2 3 π π π θ = = Example 2 1 sin : equation the Solve = θ We want all angles having sine equal to the value given. The solution set will be an infinite set of angles since the sine function is periodic of period 2π. What is the reference angle of θ? . 6 in angle reference the , 2 1 sin Since π θ  = We start by solving the equation for one revolution. Sine is negative in quadrants 3 and 4....
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.
 Fall '08
 GARDNER
 Calculus, PreCalculus, Equations, Angles

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